Periodic Orbit Description of Nonadiabatic Quantum Dynamics

Abstract

Classical periodic orbits associated with the nonadiabatic dynamics of a spin-boson-type problem are introduced. To facilitate a classical description of spin states, the formulation employs an exact mapping of the discrete quantum variables onto continuous degrees of freedom. Adopting a one-dimensional spin-boson model, the shortest periodic orbits of the problem are identified and used to analyze the nonadiabatic quantum dynamics. The possibility of directly observing these vibronic periodic orbits in femtosecond time-resolved experiments is discussed.

Quasiperiodic orbit analysis of nonadiabatic cis–trans photoisomerization dynamics

“…Furthermore, there are numerous, mostly irregular, orbits that propagate in between the adiabatic PESs. Interestingly, these findings are quite similar to previous periodic-orbit studies of an electron-transfer system, 19 thus indicating that this classification may be quite generic.…”

“…Similar to previous studies of a onedimensional electron-transfer system, 19 there are various orbits that predominantly evolve on a single adiabatic PES: Rotating orbits and cis and trans oscillating orbits in the electronic ground state, as well as orbits oscillating in the excited-state potential well between the cis and trans configuration. Furthermore, we have discussed various orbits that propagate in between adiabatic PESs.…”

“…We have identified the shortest of these periodic orbits, which were also found to be most important for the interpretation of nonadiabatic quantum dynamics. [19][20][21] Adopting the adiabatic electronic representation, these vibronic periodic orbits could be characterized in a simple and physically appealing way. First, there are periodic orbits that evolve predominantly on a single ͑either the lower or the upper͒ Born-Oppenheimer surface.…”

“…With this end in mind, we have recently investigated the classical phase space of a nonadiabatically coupled system and also introduced the classical periodic orbits of such a system. [19][20][21] Periodic orbits, i.e., solutions of the classical equation of motion that return to their initial conditions, are of particular interest, because they can be directly linked to spectral response functions via semiclassical trace formulas. 22 Because periodic-orbit theory allows us to express quantum observables in terms of classical trajectories, it represents an appealing tool to analyze complicated or elusive quantum phenomena with the aid of intuitively clear classical concepts.…”

“…[22][23][24][25][26][27][28][29] Adopting a simple model of intramolecular electron transfer, we have identified the shortest periodic orbits of the system and used them to analyze the nonadiabatic quantum dynamics. 19 In particular, it has been demonstrated that transient oscillations observed in electron-transfer femtosecond experiments may be explained in terms of a few classical trajectories. 21 So far, we have restricted our studies to a highly idealized spin-boson-type model, i.e., to an electronic two-state system with constant interstate coupling and a single linearly shifted harmonic vibrational mode.…”